Polar Coordinates

Trivium

1. Given an origin point and a coordinate axis in the plane, use a protractor and ruler to determine the polar coordinates of any point in that plane.
2. Given either the rectangular or polar coordinates of a point in space write down its coordinates in the other system.
3. Given an angle expressed in radian, or in degrees/minutes/seconds, or as a fraction of a degree, express it the other two ways.
4. Given an analytic description (equation) of a curve in either rectangular or polar coordinates, write down a description in the other coordinate system.

Problems & Challenges

1. What is the distance between the points \((3,45°)?\) and \((5,210°)?\)

   In general, given two points \((r_1, \theta_1)\) and \((r_2, \theta_2),\) what is a formula for the distance between them?